Formulas - questions

1 - What is the formula for density and what unit does it have ?

2 - You measure two values a and b with the errors Δa and Δb .
Then you calculate a new quantity y = a + b.
What is the error on y ?

3 - You measure two values a and b with the errors Δa and Δb .
Then you calculate a new quantity y = a - b.
What is the error on y ?

4 - You measure three values a, b and c with the errors Δa , Δb and Δc .
Then you calculate a new quantity y = ab/c .
What is the error on y ?

5 - What is the formula for acceleration ?

6 - What is the average speed and velocity ?

7 - What is the SUVAT formulas for uniform acceleration ?

8 - How do you calculate the force W (the weight) ?

9 - What is momentum ?

10 - What is impulse ?

11 - What is Newton's second law of motion ?

12 - What is kinetic energy ?

13 - What is potential energy ?

14 - What is total energy ?

15 - What is power ?

16 - What is efficiency ?

17 - What is the formula for frequency and period ?

18 - What is angular velocity ?

19 - What are the formulas for the centripetal force ?

20 - Harmonic oscillator: What are the formulas for (1) displacement as a function of time (2) velocity as a function of time and (3) acceleration as a function of time ?

21 - Harmonic oscillator: What is the maximum displacement, velocity and acceleration ?

22 - Harmonic oscillator: What is the formula for velocity as a function of displacement ?

23 - Harmonic oscillator: What is the formula for acceleration as a function of displacement ?

24 - Harmonic oscillator: What are the formulas for (1) kinetic energy as a function of time and (2) kinetic energy as a function of displacement.

25 - Harmonic oscillator: What are the formulas for (1) total energy as a function of time and (2) total energy as a function of displacement.

26 - Harmonic oscillator: What are the formulas for (1) potential energy as a function of time and (2) potential energy as a function of displacement.

27 - How can the wavelength for a wave be calculated from the period and the wave speed ?

28 - What is Snell's law ?

29 - What are the formulas for doppler effect and sound ?

30 - What is the formula for doppler effect with EM radiation such as light ?

31 - What is the formula for doppler effect if you work with wavelength ?

32 - Draw a picture of a diffraction measurement and the formulas.

33 - Draw a picture of a resolution measurement and the formulas.

34 - What is Malus's law ?

35 - What is Brewster's angle ? Draw a picture and give the formula.

36 - What is the formula for thermal capacity ?

37 - What is the formula for specific heat capacity ?

38 - What is the relationship between thermal capacity and specific heat capacity ?

39 - What is the formula for specific latent heat ?

40 - How is power defined when it is used for thermal problems ?

41 - What is Newton's law of gravitation ?

42 - What is gravitational field strength ?

43 - What is gravitational field strength close to a sphere with a mass ?

44 - What is Coulomb's law of electrical fields ?

45 - What is electrical field strength ?

46 - What is electrical field strength close to a sphere with a charge Q ?

47 - What is the formula for a wire with a current that is placed in an external magnetic field ?

48 - What is the formula for free charge that moves in an external magnetic field ?

49 - What is the formula for work ?

50 - What is the formula for electric potential difference ?

51 - Define current !

52 - What is Ohms law ?

53 - What is the formula for resistivity ?

54 - What is the formula for a battery with internal resistance ?

55 - What is power and what is its unit ?

56 - What is the formula for the power delivered by a battery ?

57 - What is the formula for the power dissipated by a resistor ?

58 - What is the formulas for resistors coupled in series and parallel ?

59 - What is the formula for acceleration of an electron or proton over a potential difference ?

60 - What is Einstein's famous formula and what does it mean ?

61 - What does the decay equation that give the decay curve look like ?

62 - What is the relationship between the decay constant and the half-life ?

63 - What does the activity equation look like ?

64 - Fill in this table:

65 - What is the formula for photoelectric effect ?

66 - What is the formula for Millikan's photoelectric experiment ?

67 - What is the formula for the atom box model ?

68 - What is Heisenberg's uncertainty relations ?

69 - What is the formula for solar intensity ?

70 - What is the formula for albedo ?

71 - Calculate the power of a hydroelectric station.

72 - Calculate the power of a wind power station.

73 - Calculate the power of a wave power station.

74 - What is the formula for the sun's intensity hitting a planet ?

75 - What is the Stefan-Boltzmann's formula ?

76 - What is the formula for surface heat capacity ?

77 - What is the formula for temperature change due to solar radiation ?

78 - What is the formula for the coefficient of volume expansion ?

Formulas

Density: ρ = m / V where m is the mass and V is the volume. Unit: kg/m³

If you measure two values a and b with the errors Δa and Δb and you calculate a new quantity y = a + b.
Then you find the error on y in the data booklet:

If you measure two values a and b with the errors Δa and Δb and you calculate a new quantity y = a - b.
Then you find the error on y in the data booklet:

If you measure three values a, b and c with the errors Δa , Δb and Δc and you calculate a new quantity y = ab/c .
Then you find the error on y in the data booklet:

Acceleration is a vector. It is defined as Acceleration = change of velocity / time . Unit = m/s² .

Formula: a = (v - u) / Δt
where v is the velocity at time t₁ and u the velocity at time t₂ and Δt = t₂ - t₁

Average speed and velocity is when one averages over a long time (t). During this time the velocity and speed might go up and down.
The formula to use for the calculation is v = s / t where s is displacement if the velocity is calculated and s is distance if the speed is calculated.

First look at the data booklet:

The force W (the weight) is calculated from W = m•g = mass x 9.81 (Unit: N)

If you have forgotten the value of g you can find it in the data booklet.

Look at the data booklet:

Momentum is defined as the product of mass and velocity: p = m•v = mass x velocity (Unit: kg m/s or Ns)

Look at the data booklet:

Impulse is defined as the change of momentum: I = Δp = mv_final - mv_initial (Unit: kg m/s)

Newton's second law of motion:

Look at the data booklet:

Version 1.
i) An unbalanced force acting on an object causes its momentum (p = m•v) to change.
ii) The rate of the momentum change is proportional to the force and will be in the same direction as the force

Look at the data booklet:

Version 2.
i) An unbalanced force acting on an object causes it to accelerate.
ii) The acceleration is proportional to the force and will be in the same direction as the force (F=a•m → a = F / m).
iii) The acceleration is inversely proportional to the mass (F=a•m → a = F / m).

Look at the data booklet:

Kinetic energy is the mechanical energy a body has due to its movement.

E_k = mv²/2

Look at the data booklet:

Potential energy is the mechanical energy a body has due to its position above the earth.

ΔE_p = mgΔh where Δh is the difference in height between two locations and g = 9.81 .

There are also other forms of potential energy due to for example a bodys position in an electric field.

The total mechanical energy: E_t = E_k + E_p

This total energy is constant unless the energy is transformed into another form of energy which is not mechanical, such as heat.

Look at the data booklet:

Power: P = W / t → Power = work done per unit time Unit: Watt (W) or J/s

P = W / t = F•Δs/t = F•v where v is the average velocity.

When one is working with heat the formula changes to P = Q / t where Q is the heat.

ε = W_out / W_in → Efficiency = useful work out / energy put in Unit: %

The frequency (f) is the number of periods per unit time. Unit: Hz or s^-1

f = 1 / T and T = 1 / f

Look at the data booklet:

The angular velocity (ω) is the angle per unit time.

ω = 2π / T since the angle for a complete turn is 2π

ω = 2π / T = 2π•f since f = 1 / T

Look at the data booklet:

Look at the data booklet:

Look at the data booklet:

Look at the data booklet:

Look at the data booklet:

Note that total energy do not depend on time or displacement because it is constant and always the same whatever the time or displacement is.

Look at the data booklet:

Velocity = distance / time

v = λ / T

Look at the data booklet:

where n is the refractive index. n = 1 for air (vacuum).

Look at the data booklet:

Doppler effect for EM radiation

Look at the data booklet:

Look at the data booklet:

If polarized light with intensity I₀ hits a polarizor with an angle between the axis of the polarized light and the polarizor that is θ, then I is the intensity of the light that gets out from the polarizor.

Look at the data booklet:

The relationship between thermal capacity and specific heat capacity is:

C = c m

Look at the data booklet:

P = Q / t

Look at the data booklet:

Look at the data booklet:

Look at the data booklet:

Look at the data booklet:

Look at the data booklet:

F = B•I•L
Where B is the magnetic flux density in Tesla, I is the current in Amperes and L is the length of the wire in meters and F is the force in Newtons.
If the field is not perpendicular to the current but there is and angle θ between the current and the field then the formula changes to:
F = B•I•L•sin(θ)

Look at the data booklet:

F = B•q•v
Where B is the magnetic flux density in Tesla, q is the charge in Coulomb and v is the velocity in m/s and F is the force in Newtons.
If the field is not perpendicular to the velocity but there is and angle θ between the velocity and the field then the formula changes to:
F = B•q•v•sin(θ)

Look at the data booklet:

Work: W = F•Δs = Force x Distance moved in the direction of the force

The unit for potenial is Volts (V)
The unit for work is the same as for energy: Joule (J)
The unit for charge is Coulomb (C)

Look at the data booklet:

The current (I) is the flow of charge (Δq) from the positive end of a battery to the negative end per unit time (Δt).
1 Ampere of current = 1 Coulomb of charge passing through a wire in one second.

Look at the data booklet:

The unit for resistance is ohm (Ω). One ohm is the amount of electrical resistance that exists in an electrical circuit when one amp of current is flowing with one volt being applied to the circuit.

Look at the data booklet:

The unit for resistivity is Ωm.

The formula describes how the resistance depends on the length of a wire (L) and its cross section area (A) with the resistivity (ρ) being the constant of proportionality.

Power: P = W / t → Power = work done per unit time Unit: Watt (W) or J/s

For a battery the power delivered is P = ε•I . The power is in this case the amount of chemical energy converted to electrical energy per unit time.

Look at the data booklet:

The power is in this case the amount of electrical energy converted to heat per unit time.

Look at the data booklet:

Look at the data booklet:

E: Energy in J
m: mass in kg
c: speed of light m/s (a constant = 300000 km/s)

The formula tells us that energy is equivalent to mass.

Look at the data booklet:

N₀: the number of radioactive nuclei at time = 0 (when the measurement starts).
N: the number of radioactive nuclei at time = t.
N/N₀: the fraction of nuclei left after a time = t.
λ: the decay constant (can be calculated from the half-life).

Look at the data booklet:

T_1/2: Half-life in s.
λ: the decay constant in s^-1.
ln(2) = 0.693....

Look at the data booklet:

N₀: the number of radioactive nuclei at time = 0 (when the measurement starts).
N: the number of radioactive nuclei at time = t.
λ: the decay constant (can be calculated from the half-life).

Another way of writing this equation is A = A₀ e^-λt

A₀=λN₀: the activity at a time = 0. Unit: Bq = Becquerel = decay / s

A: the activity at a time = t. Unit: Bq = Becquerel = decay / s

A/A₀: the fraction of the activity left after a time = t.

Look at the data booklet:

where
hf = The energy of the incoming photons.
φ = hf_o = The minimum photon energy needed to kick out an electron.
E_max = Maximum kinetic energy that the electrons can get from the photon.

Look at the data booklet:

where
hf = The energy of the incoming photons.
hf₀ = The minimum photon energy needed to kick out an electron.
e = The elementary charge = 1.60x10^-19C (see databooklet).
V = The voltage needed to make the current zero.

Look at the data booklet:

where
L = The length of the box.
E_k = The kinetic energy of the electrons.
n = The number of nodes.
h = Plancks constant (see databooklet).
m_e = The mass of an electron (see databooklet).

Look at the data booklet:

Look at the data booklet:

Δp : The precision (error) of a measurement of momentum
Δx : The precision (error) of a measurement of position
ΔE : The precision (error) of a measurement of energy
Δt : The precision (error) of a measurement of time

Heisenberg's uncertainty principle says that one cannot measure momentum and position of a particle (or energy and time) to any precision. There is a limit to how well one can know these things.

Look at the data booklet:

where
I = intensity
A = area

so the intensity is defined as the power of the radiation divided with the area that it hits.

Look at the data booklet:

so the albedo is the fraction of the incoming solar power that is reflected away.

Calculating the power of a hydroelectric station

One gets the power from the change of the potential energy of the water per unit of time as it falls down and hits the turbine:

P = mgh / t where

P = power
m = mass of the water
g = gravitational constant
h = the height that the water falls
t = time

we can modify this formula by using the formula for density (ρ = m/V = 1000 kg/m³):

P = mgh / t = ρVgh / t

the quantity V/t is called the volume flow rate.

Calculating the power of a wind power station

The power can be calculated from the kinetic energy of the air moving through the propeller:
Look at the data booklet:

where
ρ = density of air (1.2 kg/m³)
A = area of the propeller
v = velocity of the wind

Calculating the power of a waves

The power per unit length of a wave is:
Look at the data booklet:

where
ρ = density of water (1000 kg/m³)
g = gravitational constant
A = amplitude (height) of the waves.
v = velocity of the waves.

I = I_sun / 4πd² where
I_sun=3.9x10²⁶ W is the power radiated from the sun.
I = the intensity of the sun's radiation hitting a planet.
d = the distance from the sun to the planet.

Stefan-Boltzmanns law

Look at the data booklet:

Where the constant σ can also be found in the data booklet:

The Stefan-Boltzmann law gives the total power emitted by a black body with surface area A if it has the temperature T.

Emmisivity (e) is a parameter that tells us how close a solid is to a perfectly black object. It can have values between 0 and 1 where e=0 is not a black object at all and e=1 is a perfectly black object.

The surface heat capacity

The surface heat capacity C_s is the amount of heat (Q) in an area of 1 m² that is needed to raise the temperature of the ground with 1 Kelvin.
Look at the data booklet:

where
A = Area of the ground.
Q = Heat energy.
ΔT = Change in temperature.

Look at the data booklet:

where
ΔT = Change in temperature.
C_s = the surface heat capacity.
I_in = the incoming intensity of the solar radiation.
I_out = the outgoing intensity of the solar radiation.
t = time

where
β = the coefficient of volume expansion.
ΔT = Change in temperature of a liquid.
V₀ = the original volume of the liquid before the temperature changed.
ΔV = Change of volume of a liquid.

So β is a constant that tells how much a liquid will expand when the temperature change with ΔT.